README.md

PDECharactSimulink

Solving partial differential equations (PDEs) in Simulink with the method of characteristics.

First-order quasilinear (FOQL) PDEs

Library PDECharactLib.slx contains the FOQL PDE subsystem for modeling first-order quasilinear PDEs of the form $$w_t + v\big( t, x, w(t, \cdot) \big) w_x = f\big( t, x, w(t, \cdot) \big), \quad t \geq 0, \quad x \in [0, \ell]$$ with initial condition $w(0, x) = w_0(x)$ ($x \in [0, \ell]$) and boundary condition $w(t, 0) = u(t)$ ($t \ge 0$). Detailed description of the method is available at https://arxiv.org/abs/1907.13419.

Examples:

• FOQL_PDE_SimpleExample.slx: simple example of using the FOQL PDE subsystem.
• FOQL_PDE_OutputFeedback.slx: model of a heat exchanger with output feedback control, discussed in the PDF file FOQL_PDE_OutputFeedback.pdf.
• FOQL_PDE_StateFeedback.slx: example with full-state feedback, discussed in the main paper https://arxiv.org/abs/1907.13419.